In which scenario can we see the DOWN state of ospf neighbor ?

A neighbor that is discovered dynamically through reception of HELLO packets can fall back to a down state if it is being deleted, for example when OSPF does not receive HELLO packets from the neighbor for period of time longer than the Dead timer interval. 

If you dont have route in routing table, you can say when you interface is shutdown the neighbor will see down state.

Area mismatch, authentication mismatch, hello and Dead intervals mismatch